This ebook is available for the following devices:

iPad

Windows

Mac

Sony Reader

Cool-er Reader

Nook

Kobo Reader

iRiver Story

Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.

Brouwer and Brouwerian intuitionism.- Another look at Brouwer’s dissertation.- Brouwerian infinity.- The new intuitionism.- Truth and experience of truth.- The proper explanation of intuitionistic logic: on Brouwer’s demonstration of the Bar Theorem.- The intersection of intuitionism (Brouwer) and phenomenology (Husserl).- Brouwer on ‘hypotheses’ and the middle Wittgenstein.- Brouwer’s notion of intuition and theory of knowledge by presence.- Buddhist models of the mind and the common core thesis on mysticism.- Kindred spirits.- Remarks on the supposed french’ semi-’ or ‘pre-intuitionism’.- Poincaré: intuitionism, intuition, and convention.- Some of Julius König’s mathematical dreams in his New Foundations of Logic, Arithmetic, and Set Theory.- Gödel, constructivity, impredicativity, and feasibility.- Lorenzen’s operative justification of intuitionistic logic.- Mathematical perspectives.- The Hilbert-Brouwer controversy resolved?.- Proof theory and Martin-Löf Type Theory.- Some remarks on linear logic.- Two applications of dynamic constructivism: Brouwer’s continuity principle and choice sequences in formal topology.- A reverse look at Brouwer’s Fan Theorem.- Some applications of Brouwer’s Thesis on Bars.- Concluding remarks at the Cerisy conference.- A bibliography of L.E.J. Brouwer.